Finite Group Databasebeta

← C11×#8459 #14585652

Subgroups — C11×#8459 #14585652

Order 2816.

922 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 922 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#1985C211yesmaximal, characteristic, complemented
3C11×#1551C212yesmaximal, complemented
4C11×#1530C212yesmaximal, complemented
5C11×#1467C211yesmaximal, characteristic, complemented
6C2×C11×2−1+4C412yes—
7C11×#550—22no—
8D4×Q8×C11—22no—
9C11×#548—24no—
10C11×#537—22no—
11C11×#537C412yes—
12C11×#532—22no—
13C11×#532C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C11×#432C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#97C2211yescharacteristic
18C11×#336—22no—
19C11×#333—22no—
20C11×#331—22no—
21C11×#329—24no—
22C11×#324—22no—
23C11×2−1+4—48no—
24C2×C11×#41—24no—
25C2×C11×#41—24no—
26C2×C11×#41C2×C414yes—
27C22×Q8×C11—24no—
28C22×Q8×C11C2×C411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C11×C4⋊Q8—22no—
32C11×C4⋊Q8D412yes—
33C11×#127—22no—
34C11×#127D412yes—
35C11×#124—24no—
36C11×#124D414yes—
37C11×C22⋊Q8—28no—
38C11×C22⋊Q8—24no—
39C11×#121—28no—
40C11×#121—24no—
41C11×#121—24no—
42C11×#121—22no—
43C11×#121—22no—
44C4×Q8×C11—22no—
45C4×Q8×C11—22no—
46C4×D4×C11—24no—
47C4×D4×C11—24no—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C4⋊C4D412yes—
52C2×C42×C11D412yes—
53C2×C42×C11C2311yescharacteristic
54C11×C4⋊C8—22no—
55C11×C4⋊C8—22no—
56C11×C22⋊C8—22no—
57C11×#97—22no—
58C11×#97—22no—
59#8459C1111yesmaximal, characteristic, direct product factor, Sylow
60C11×#41—48no—
61C11×#41—48no—
62C11×#41—416no—
63C11×#41—48no—
64C2×Q8×C11—24no—
65C2×Q8×C11—24no—
66C2×Q8×C11—22no—
67C2×Q8×C11—416no—
68C2×Q8×C11C22⋊C414yes—
69C2×D4×C11—24no—
70C2×D4×C11—24no—
71C2×D4×C11—24no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11C22⋊C414yes—
75C22×C4×C11—28no—
76C22×C4×C11—24no—
77C22×C4×C11C22⋊C412yes—
78C22×C4×C11C22⋊C412yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—42no—
85C2×C8×C11—41no—
86C2×C8×C11—42no—
87C2×C8×C11—41no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C22⋊C4—28no—
94C11×C22⋊C4—24no—
95C11×C22⋊C4—24no—
96C42×C11—22no—
97C42×C11—22no—
98C42×C11C2×D412yes—
99C42×C11C2×D412yes—
100#3497C2×C1111yescharacteristic
101#1985C2×C1111yescharacteristic, complemented
102#1551C2×C1112yescomplemented
103#1530C2×C1112yescomplemented
104#1467C2×C1111yescharacteristic, complemented
105C23×C11—24no—
106C23×C11C2×C22⋊C411yescharacteristic
107Q8×C11—28no—
108Q8×C11—44no—
109Q8×C11—48no—
110D4×C11—44no—
111D4×C11—48no—
112D4×C11—48no—
113D4×C11—42no—
114D4×C11—42no—
115D4×C11—82no—
116D4×C11—84no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—41no—
125C2×C4×C11—416no—
126C2×C4×C11—48no—
127C2×C4×C11—42no—
128C2×C4×C11#10014yes—
129C2×C4×C11C2×C22⋊C412yes—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12012yes—
132C2×C4×C11#12011yescharacteristic
133C8×C11—42no—
134C8×C11—82no—
135C8×C11—81no—
136C2×2−1+4C4×C1112yes—
137#550—22no—
138D4×Q8—22no—
139#548—24no—
140#537—22no—
141#537C4×C1112yes—
142#532—22no—
143#532C22×C1112yes—
144C2×C4×Q8C22×C1111yescharacteristic
145#432C22×C1112yes—
146C2×C4⋊C8C22×C1111yescharacteristic
147C2×#97C22×C1111yescharacteristic
148#336—22no—
149#333—22no—
150#331—22no—
151#329—24no—
152#324—22no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—44no—
156C22×C11—44no—
157C22×C11—44no—
158C22×C11#37911yescharacteristic
159C22×C11C2×#10012yes—
160C4×C11—21no—
161C4×C11—22no—
162C4×C11—24no—
163C4×C11—22no—
164C4×C11—42no—
165C4×C11—44no—
166C4×C11#45411yescharacteristic
167C4×C11#45611yescharacteristic
1682−1+4—48no—
169C2×#41—24no—
170C2×#41—24no—
171C2×#41C2×C4×C1114yes—
172C22×Q8—24no—
173C22×Q8C2×C4×C1111yescharacteristic
174C22×C8—21no—
175C22×C8—21no—
176C4⋊Q8—22no—
177C4⋊Q8D4×C1112yes—
178#127—22no—
179#127D4×C1112yes—
180#124—24no—
181#124D4×C1114yes—
182C22⋊Q8—28no—
183C22⋊Q8—24no—
184#121—28no—
185#121—24no—
186#121—24no—
187#121—22no—
188#121—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×D4—24no—
192C4×D4—24no—
193C4×D4—22no—
194C4×D4—22no—
195C2×C4⋊C4C2×C4×C1111yescharacteristic
196C2×C4⋊C4D4×C1112yes—
197C2×C42D4×C1112yes—
198C2×C42C23×C1111yescharacteristic
199C4⋊C8—22no—
200C4⋊C8—22no—
201C22⋊C8—22no—
202#97—22no—
203#97—22no—
204C2×C11—22no—
205C2×C11—84no—
206C2×C11#178311yescharacteristic
207C2×C11#179311yescharacteristic
208C2×C11#179411yescharacteristic
209#41—48no—
210#41—48no—
211#41—416no—
212#41—48no—
213C2×Q8—24no—
214C2×Q8—24no—
215C2×Q8—22no—
216C2×Q8—416no—
217C2×Q8C11×C22⋊C414yes—
218C2×D4—24no—
219C2×D4—24no—
220C2×D4—24no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4C11×C22⋊C414yes—
224C22×C4—28no—
225C22×C4—24no—
226C22×C4C11×C22⋊C412yes—
227C22×C4C11×C22⋊C412yes—
228C22×C4C22×C4×C1111yescharacteristic
229C22×C4C2×D4×C1111yescharacteristic
230C22×C4C2×D4×C1111yescharacteristic
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—41no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—24no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C22⋊C4—28no—
243C22⋊C4—24no—
244C22⋊C4—24no—
245C42—22no—
246C42—22no—
247C42C2×D4×C1112yes—
248C42C2×D4×C1112yes—
249C11#845911yescharacteristic, direct product factor, Sylow
250C23—24no—
251C23C2×C11×C22⋊C411yescharacteristic
252Q8—28no—
253Q8—44no—
254Q8—48no—
255D4—44no—
256D4—48no—
257D4—48no—
258D4—42no—
259D4—42no—
260D4—82no—
261D4—84no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—41no—
270C2×C4—416no—
271C2×C4—48no—
272C2×C4—42no—
273C2×C4C11×#10014yes—
274C2×C4C2×C11×C22⋊C412yes—
275C2×C4C11×#12011yescharacteristic
276C2×C4C11×#12012yes—
277C2×C4C11×#12011yescharacteristic
278C8—42no—
279C8—82no—
280C8—81no—
281C22—21no—
282C22—21no—
283C22—44no—
284C22—44no—
285C22—44no—
286C22C11×#37911yescharacteristic
287C22C2×C11×#10012yes—
288C4—24no—
289C4—22no—
290C4—21no—
291C4—22no—
292C4—44no—
293C4—42no—
294C4C11×#45411yescharacteristic
295C4C11×#45611yescharacteristic
296C2—22no—
297C2—84no—
298C2C11×#178311yescharacteristic
299C2C11×#179311yescharacteristic
300C2C11×#179411yescharacteristic
subgroupG/H
center, socleC22×C11#379
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3497C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#1985C2semidirect
3. C11×#1551C2semidirect
4. C11×#1530C2semidirect
5. C11×#1467C2semidirect
59. #8459C11direct (N × H)
101. #1985C2×C11semidirect
102. #1551C2×C11semidirect
103. #1530C2×C11semidirect
104. #1467C2×C11semidirect
249. C11#8459direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#34972
C11×#19852
C11×#15512
C11×#15302
C11×#14672
#845911